Question

use the data in the following table, which lists survey results from high school drivers at least 16 years of age. assume that subjects are randomly selected from those included in the table.

	drove when drinking alcohol?
texted while driving	652	3098
no texting while driving	189	4260

if four different high school drivers are randomly selected, find the probability that they all drove when drinking alcohol.
the probability that four randomly selected high school drivers all drove when drinking alcohol is
(round to six decimal places as needed.)

Explanation:

Step1: Calculate total number of drivers

$652 + 3098+189 + 4260=8200$

Step2: Calculate number of drivers who drove when drinking alcohol

$652+189 = 841$

Step3: Calculate probability of first - selected driver drove when drinking alcohol

The probability $P_1=\frac{841}{8200}$

Step4: Calculate probability of second - selected driver drove when drinking alcohol (without replacement)

After one driver is selected, there are 839 remaining drivers who drove when drinking alcohol and 8199 total remaining drivers. So $P_2=\frac{840}{8199}$

Step5: Calculate probability of third - selected driver drove when drinking alcohol (without replacement)

After two drivers are selected, there are 838 remaining drivers who drove when drinking alcohol and 8198 total remaining drivers. So $P_3=\frac{838}{8198}$

Step6: Calculate probability of fourth - selected driver drove when drinking alcohol (without replacement)

After three drivers are selected, there are 837 remaining drivers who drove when drinking alcohol and 8197 total remaining drivers. So $P_4=\frac{837}{8197}$

Step7: Calculate the probability that all four drove when drinking alcohol

$P = P_1\times P_2\times P_3\times P_4=\frac{841}{8200}\times\frac{840}{8199}\times\frac{838}{8198}\times\frac{837}{8197}\approx0.001077$

Answer:

$0.001077$